New York’s prime place in cinema is about far more than the city’s generous tax credit. There’s just something about stories set here that excites filmmakers and audiences alike. The list of great New York movies is as long as Broadway itself. From “The Naked City” to “Rosemary’s Baby” to “Gangs of New York,” Gotham has served as a backdrop for some of the most memorable and influential movies in history.

On the occasion of the Blu-ray releases of Woody Allen’s “Manhattan” and “Annie Hall” — two classic city flicks unavailable in high definition until now — The Post assembled a list of 10 definitive New York movies in relation to what they say about the city and we who live in it. Here they are, in no particular order. Let the debating begin.

“This city is an open sewer. It’s full of filth and scum,” says Travis Bickle, the psychotic loner in Martin Scorsese’s pitch-black urban revenge story. Anyone who lived through New York in the 1970s can relate. Times Square was a cess pit. Crime was rampant. Trash lined the streets. Drugs were everywhere. The city needed a hero. What it got was a mohawked man with a pistol.

Bickle, played by De Niro, cruised the dirty streets at night, popping pills to stay awake, his only friend a teen hooker (Jodie Foster).

Screenwriter Paul Schrader has said the movie grew out of a dark period when he’d left his job, had no place to live and saw his marriage collapsing. “Out of this funk emerged this notion of a taxi driver, this guy in a metal coffin floating through the sewers, the streets,” Schrader says on the DVD’s special features.

Looking at the mall that Manhattan has become, it’s easy to forget how different the city once was. “Taxi Driver” will never let us forget.

2 “Working Girl” (1988) Anyone can make it in NYC, even a secretary

One morning in 1984, writer Kevin Wade and producer Douglas Wick were standing in Battery Park watching folks on their way to work. “Everywhere we looked, Kevin and I noticed smart-looking, pretty young women rushing to work in tennis shoes and carrying high heels,” Wick told AFI.com. “We started talking about them and realized that they all must have a story.”

Thus was born Tess McGill (Melanie Griffith), a secretary at a Manhattan brokerage firm who impersonates her absent boss (Sigourney Weaver) to close a mega deal. The movie was a Cinderella-esque tale about a woman succeeding in an industry that was overwhelmingly male.

“It’s a story about the American Dream’s implicit promise that the door is open to anybody who has the smarts,” Wade said. “And how America has evolved into a class system where white Anglo-Saxons run the country, and how hard it would be for someone like Tess to break through that.”

3 “Manhattan” (1979) We love our town — the rest of you can go home

Woody Allen is synonymous with New York and “Manhattan” is arguably his most New York-y film. He shot it in black-and-white, he claimed, because that’s how the city appeared in his memories.

The famous opening sequence, a collection of artistic shots of the city’s skyline and fireworks exploding over Central Park, was meant to be Allen’s love letter to the city at a time when many films, such as “The Warriors” and “Death Wish,” were portraying New York as a crime-ridden Gomorrah.

“For some reason I’ve always had an irrational love for New York,” Allen told New York magazine. “It’s very expensive. Very little of it works. But the city is so full of chaos, and the chaos is, for many people, pleasurable.”

In “Manhattan,” he finds that pleasure eating at Elaine’s, visiting museums and walking the streets, turning the city into perhaps the film’s most memorable character.

Johnny Depp was originally going to play Patrick Bateman, an empty, vain, status-obsessed banker who also happens to be a serial killer. When Depp dropped out, filmmakers considered Leonardo DiCaprio, who eventually walked away because, legend has it, Gloria Steinem urged him to consider his young female fans and how they’d react to seeing him taking a chain saw to women. Christian Bale ultimately stepped in and played the part to perfection, basing the character on Tom Cruise.

The 1991 Bret Easton Ellis novel upon which the film was based was hugely controversial at the time. Many considered its graphic violence misogynistic. But writer-director Mary Harron understood that the story was wicked satire, an indictment of the out-of-control consumer culture that was perfectly embodied by big-spending Wall Streeters.

“A lot of it had to do with my frustration with what it meant to be an adult male in American society,” Ellis told Publishers Weekly. “Consumerist success was really the embodiment of what it meant to be a cool guy: money, trophy girlfriends, nice clothes and cool cars. It all seemed extremely shallow.”

5 “Wild Style” (1983) The world loves authentic NYC culture

In the late 1970s in the South Bronx, amidst the abandoned buildings and rubble-strewn lots, a vibrant subculture was bubbling up in the streets: hip-hop. “Wild Style,” which began filming in 1981, wasn’t a documentary, but it ended up being one of the most important records of the early days of New York’s rap, graffiti and break-dancing scene.

The movie played a huge role in popularizing hip-hop around the world — and even to the rest of the city, where many residents weren’t even aware of it.

“Maybe they’d heard about the scene, but it had never been put together where people could sit down and analyze and say, ‘OK, this is what it is,’ ” says Easy A.D., a member of hip-hip pioneers Cold Crush Brothers, who are featured in “Wild Style.”

The movie opened in 1983 at a Times Square theater and kids from all five boroughs lined up. The film was also huge overseas, allowing Cold Crush Brothers to tour Japan, where they were mobbed by Asian teens dressed in b-boy gear.

“Turkish kids came out when we showed it in Berlin,” says writer-director Charlie Ahearn. “They identified with the underclass of society. I continued to be amazed at the depth of identification. People were hungry for something that felt authentic.”

6 “On the Town” (1949) NYC has always been on the cutting edge

The Frank Sinatra-Gene Kelly musical may appear quaint today, but back in 1949, MGM deemed the Broadway musical upon which the film was based too bold for mainstream audiences. This was a show about New York for New Yorkers and then, as now, what works here doesn’t necessarily work in the rest of America. We wouldn’t have it any other way.

“MGM thought it was too racy or dirty or sexy, and they thought the music by Leonard Bernstein was too avant-garde,” says Jane Feuer, a professor of film studies at the University of Pittsburgh and author of “The Hollywood Musical.” Many of the original songs were replaced. The lyric “New York, New York, it’s a helluva town” was swapped out for “a wonderful town.” And a plotline about Kelly’s character hailing from Indiana was added.

Even with changes, the film about three sailors on 24-hour shore leave still presents the Big Apple as far more advanced than the rest of America, especially when it comes to women.

“The women in it are much more like women today,” Feuer says. “They’re more urban and aggressive. They drove taxis. They were oversexed. They came to New York to become dancers, but wound up performing burlesque in Coney Island.”

7 “A Bronx Tale” (1993) We learn more on the streets than in school

Chazz Palminteri recently traveled to South America where people at the airport started calling him “the bad man” in Spanish. Turns out they were fans of the writer-actor’s coming-of-age drama about a teen (Lillo Brancato) who befriends a local mob boss (Palminteri), much to the chagrin of his father (Robert De Niro, who directed).

Palminteri says the movie is “75 to 80 percent” autobiographical and was his attempt to capture his time growing up near Arthur Avenue in the ’50s and ’60s — including the racism and mob culture. The young hero gains wisdom not in the classroom, but on the streets, including a famous lesson from the mob boss about dumping any girl who won’t unlock a door for a man when she’s sitting inside.

“You’re exposed to all these characters growing up in The Bronx,” says Palminteri, who’s taking a stage version of “A Bronx Tale” to Las Vegas in March. “Back then, I walked outside and I had 25 friends on the corner. Then there were 25 older guys we hung around with, and 25 wiseguys. There were so many people to feed from, to learn from, to sponge from.”

8 “When Harry Met Sally” (1989) For better or worse, we’re a town of single people

A recent study by the Census Bureau found that New York state has the highest percentage of never-married women in the country. Singles dominate city life, and maybe that’s why every romantic comedy seems to be set here. One of the form’s high-water marks is “When Harry Met Sally . . .” (original title: “Boy Meets Girl”), a breezy tale about two friends (Billy Crystal, Meg Ryan) who become more.

The movie finds the couple discussing relationships on the city’s streets, in Central Park and, most famously, in Katz’s Deli, where Ryan eats something that really, really agrees with her.

The script grew out of the personal experiences of writer Nora Ephron and director Rob Reiner, who was frustrated by single life after divorcing Penny Marshall.

“I was writing about my 10 years of floundering through my dating life and not figuring out how to be with a woman,” Reiner told AFI.

Originally, Crystal and Ryan didn’t wind up together in the finale. The bitter Reiner couldn’t imagine anyone finding true love, but during the production, he met his future wife and changed his mind and the movie’s ending.

9 “Do the Right Thing” (1989) Sometimes the melting pot melts down

Spike Lee was prompted to write his incendiary film by an infamous 1986 Howard Beach incident, in which three black men were chased out of a pizzeria by a gang of white youths. One of the black men was hit by a car and died. “We were trying to depict realistically what was the state of racial relations in the United States of America at the time,” says Lee on the DVD’s commentary.

The movie takes place over a scorching summer day and was shot almost entirely on a single block in Brooklyn. It features a memorable cast, including Lee, Rosie Perez, Ruby Dee and Ossie Davis, as well as Danny Aiello and John Turturro as racist pizzeria owners.

The movie has become a classic for its blunt depictions of racial tensions within the city, but when it was released, some reviewers suggested it would lead to actual race riots. It didn’t.

10 “Sabrina” (1954) Rich and poor rub elbows in our town

By its nature, NYC forces people of all different backgrounds to mix. The rich may have bigger apartments, but everybody shares the misery of a jam-packed subway car.

In “Sabrina,” Audrey Hepburn is caught in a love triangle with the wealthy sons (Humphrey Bogart and William Holden) of her father’s boss, despite their dad’s warning about dallying with the servants.

Filming took place in New York City, and at Paramount president Barney Balaban’s mansion on Long Island. The atmosphere on set was tense. Bogart clashed frequently with director Billy Wilder, and Hepburn began having an affair with the married Holden. Despite the behind-the-scenes drama, the film became a hit. It also earned six Oscar nominations, including a Best Actress nod for Hepburn and Director for Wilder.